A logistic type equation in RN with a nonlocal reaction term via bifurcation method

We study the existence of positive solutions of a logistic equation in the entire space with a nonlocal reaction term. Mainly, we apply a bifurcation method and singular boundary equations to obtain a priori bounds of the solutions. Our results show a drastic change of behaviour of the set of positive solutions depending on the sign of the nonlocal term. (c) 2020 Elsevier Inc. All rights reserved.

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This study investigates the existence of positive solutions of a logistic equation in the entire space with a nonlocal reaction term. By applying a bifurcation method and singular boundary equations, a priori bounds of the solutions are obtained. The results show a significant change in the behavior of the set of positive solutions depending on the sign of the nonlocal term.